Sharp results regarding the asymptotic limits of adaptive experiments were worked out decades ago. The asymptotic efficiency limits in unstructured bandit problems were worked out by [1]}, and extended soon thereafter to structured parametric bandits and control of structured Markov chains by [2]}, [3]}, [4]}. The aforementioned papers focus on the reward earned during the experiment. Much earlier work by [5]}, [6]} works out closely related asymptotic limits for adaptive experiments where the emphasis is on the quality of decision post-experiment. These papers characterize complexity through a game between an player and nature. This game has a special structure in the problem of selecting the best arm, and specialized results in that case are given in [7]}, [8]} and revisited more recently in [9]}. See [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]} or [19]} for recent work along these lines .
